I am learning about equivalence classes and I need little help beacuse it's a little bit abstract for me to understand it.
This is how I understand it, and don't mind if it's not strict math.
Equivalence classes are forming subsets of equal elements from set. Since there are elements in set that are in equivalence relation it is possible to group those equal elements in groups which are actually called equivalence classes. For example, relation "=" form equivalence classes [1,1],[2,2],[3,3],[4,4],[5,5]... in N. In books there is often an example of relation congruence modulo 2 for explaining equivalence classes. So, equivalence classes are actually a way to group all elements that are equal among themselves.
Am I right, did I understand equivalence classes correctly?
Now, I need also explanations of definition in book about equivalence class.
Definiton of equivalence class:
If is relation of equivalence, then class of element , shown as symbol , defines like: